Alleviating the Effects of Light Scattering in Multivariate Calibration of Near-Infrared Spectra by Path Length Distribution Correction

Near-infrared (NIR) spectroscopy has been used for noninvasive measurements of solid and liquid samples, through highly scattering media such as colloids, food, and tissue. It has seen many applications in agriculture, medicine, and petroleum industries, mainly due to the minimal sample preparation that is required. This minimal sample preparation does come at a cost to the analyst, since the high signal-to-noise ratio of a typical NIR instrument can be riddled with effects stemming from heterogeneity and the scattering of light. This work proposes a novel preprocessing method, the path length distribution correction (PDC) method, to correct spectral nonlinearities in samples of highly scattering media. These nonlinearities stem from the distribution of path lengths of the incident light, which are a result of the scattering of light in the sample. Recent developments in time-of-flight (TOF) spectroscopy have allowed for the acquisition of the distribution of times that photons travel within a sample simultaneous with the collection of the NIR spectrum. The TOF distribution is used to estimate a path length distribution within a sample, which is then used to fix the measurement spectra, giving each spectrum an apparent path length of unity. The PDC-corrected spectra can then be used with traditional multivariate calibration methods such as principal component regression (PCR) and partial least squares (PLS). Another discussion looks at the viability of using a lognormal distribution as a simple approximation of the TOF distribution. This would be very useful in circumstances in which experimental TOF distributions are not collected. PDC is shown to significantly improve prediction errors in experimental data sets, while diagnostic plots indicate that the corrected spectra do appear to have a path length of unity, thus alleviating effects of the distribution of path lengths.